FIGS. 1 and 2 of the drawings illustrates a conventional waste container comprising an outer container 5, a cover 6, and an inner container 1 mounted in the outer container 5. The inner container 1 includes a peripheral wall 3 and a peripheral end edge 2 that delimits an upper opening. In use, a plastic bag 4 is usually placed in the inner container 1, with a peripheral edge of the plastic bag 4 extending outward across the peripheral end edge 2 and then downward. The exposed peripheral edge of the plastic bag 4 fails to provide an aesthetically pleasing effect. When the plastic bag 4 is full of waste (including garbage or the like) that is too heavy for the plastic bag 4 to withstand, the plastic bag 4 is liable to break while it is lifted, leading to contamination of the inner container 1. To solve this problem, the inner container 1 is carried to a desired location, and the plastic bag 4 is then packed and discarded. To move the inner container 1 with heavy waste, the user has to hold the inner container 1 at two sides of the peripheral end edge of the inner container 1 with both hands. Hence, the user walks with difficulty and might get hurt while carrying the inner container 1 containing heavy waste.